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M-ALG-007-WS01 · Foundation & Higher

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Worked answers · 34 questions

Student worksheet (PDF)All worked solutions (PDF)

Retrieval

  1. R01Calculate 6 × 7.

    M-ALG-007-WS01-R01

    Answer
    42
    Worked steps
    1. 6 groups of 7 make 42.

  2. R02Calculate 4 × (−3).

    M-ALG-007-WS01-R02

    Answer
    −12
    Worked steps
    1. Positive × negative is negative; 4 × 3 = 12.

  3. R03Simplify 4x + 3x.

    M-ALG-007-WS01-R03

    Answer
    7x
    Worked steps
    1. Add the coefficients: 4 + 3 = 7.

  4. R04Simplify 9y − 2y.

    M-ALG-007-WS01-R04

    Answer
    7y
    Worked steps
    1. Subtract the coefficients: 9 − 2 = 7.

Fluency

  1. F012(x + 5)

    M-ALG-007-WS01-F01

    Answer
    2x + 10
    Worked steps
    1. Multiply both terms by 2: 2 × 1x and 2 × (5).
    2. Simplify to 2x + 10.

  2. F023(x + 6)

    M-ALG-007-WS01-F02

    Answer
    3x + 18
    Worked steps
    1. Multiply both terms by 3: 3 × 1x and 3 × (6).
    2. Simplify to 3x + 18.

  3. F034(x + 2)

    M-ALG-007-WS01-F03

    Answer
    4x + 8
    Worked steps
    1. Multiply both terms by 4: 4 × 1x and 4 × (2).
    2. Simplify to 4x + 8.

  4. F045(x + 3)

    M-ALG-007-WS01-F04

    Answer
    5x + 15
    Worked steps
    1. Multiply both terms by 5: 5 × 1x and 5 × (3).
    2. Simplify to 5x + 15.

  5. F056(x + 4)

    M-ALG-007-WS01-F05

    Answer
    6x + 24
    Worked steps
    1. Multiply both terms by 6: 6 × 1x and 6 × (4).
    2. Simplify to 6x + 24.

  6. F067(x + 2)

    M-ALG-007-WS01-F06

    Answer
    7x + 14
    Worked steps
    1. Multiply both terms by 7: 7 × 1x and 7 × (2).
    2. Simplify to 7x + 14.

  7. F073(2x + 4)

    M-ALG-007-WS01-F07

    Answer
    6x + 12
    Worked steps
    1. Multiply both terms by 3: 3 × 2x and 3 × (4).
    2. Simplify to 6x + 12.

  8. F084(3x + 2)

    M-ALG-007-WS01-F08

    Answer
    12x + 8
    Worked steps
    1. Multiply both terms by 4: 4 × 3x and 4 × (2).
    2. Simplify to 12x + 8.

  9. F092(5x + 7)

    M-ALG-007-WS01-F09

    Answer
    10x + 14
    Worked steps
    1. Multiply both terms by 2: 2 × 5x and 2 × (7).
    2. Simplify to 10x + 14.

  10. F105(x − 2)

    M-ALG-007-WS01-F10

    Answer
    5x − 10
    Worked steps
    1. Multiply both terms by 5: 5 × 1x and 5 × (-2).
    2. Simplify to 5x − 10.

  11. F113(2x − 5)

    M-ALG-007-WS01-F11

    Answer
    6x − 15
    Worked steps
    1. Multiply both terms by 3: 3 × 2x and 3 × (-5).
    2. Simplify to 6x − 15.

  12. F124(3x − 2)

    M-ALG-007-WS01-F12

    Answer
    12x − 8
    Worked steps
    1. Multiply both terms by 4: 4 × 3x and 4 × (-2).
    2. Simplify to 12x − 8.

Develop

  1. D01-2(x + 5)

    M-ALG-007-WS01-D01

    Answer
    -2x − 10
    Worked steps
    1. Multiply both terms by -2: -2 × 1x and -2 × (5).
    2. Simplify to -2x − 10.

  2. D02-3(2x − 4)

    M-ALG-007-WS01-D02

    Answer
    -6x + 12
    Worked steps
    1. Multiply both terms by -3: -3 × 2x and -3 × (-4).
    2. Simplify to -6x + 12.

  3. D034(x − 3)

    M-ALG-007-WS01-D03

    Answer
    4x − 12
    Worked steps
    1. Multiply both terms by 4: 4 × 1x and 4 × (-3).
    2. Simplify to 4x − 12.

  4. D04-5(2x − 1)

    M-ALG-007-WS01-D04

    Answer
    -10x + 5
    Worked steps
    1. Multiply both terms by -5: -5 × 2x and -5 × (-1).
    2. Simplify to -10x + 5.

Apply

  1. A01A rectangle is 5 cm wide and (x + 3) cm long. Write an expanded expression for its area.

    M-ALG-007-WS01-A01

    Answer
    (5x + 15) cm²
    Worked steps
    1. Area = length × width = 5(x + 3).
    2. Multiply both terms by 5: area = (5x + 15) cm².

  2. A02Three identical tickets cost (2x + 4) pounds each. A student says the total is (6x + 4) pounds. Explain the error and give the correct total.

    M-ALG-007-WS01-A02

    Answer
    £(6x + 12)
    Worked steps
    1. Total = 3(2x + 4).
    2. The 4 must also be multiplied by 3. The total is £(6x + 12).

Independent practice

Shadow practice

  1. H012(x + 6)

    M-ALG-007-WS01-H01

    Answer
    2x + 12
    Worked steps
    1. Multiply both terms by 2: 2 × 1x and 2 × (6).
    2. Simplify to 2x + 12.

  2. H023(x + 5)

    M-ALG-007-WS01-H02

    Answer
    3x + 15
    Worked steps
    1. Multiply both terms by 3: 3 × 1x and 3 × (5).
    2. Simplify to 3x + 15.

  3. H034(x + 3)

    M-ALG-007-WS01-H03

    Answer
    4x + 12
    Worked steps
    1. Multiply both terms by 4: 4 × 1x and 4 × (3).
    2. Simplify to 4x + 12.

  4. H046(x + 2)

    M-ALG-007-WS01-H04

    Answer
    6x + 12
    Worked steps
    1. Multiply both terms by 6: 6 × 1x and 6 × (2).
    2. Simplify to 6x + 12.

  5. H052(3x + 5)

    M-ALG-007-WS01-H05

    Answer
    6x + 10
    Worked steps
    1. Multiply both terms by 2: 2 × 3x and 2 × (5).
    2. Simplify to 6x + 10.

  6. H063(4x + 2)

    M-ALG-007-WS01-H06

    Answer
    12x + 6
    Worked steps
    1. Multiply both terms by 3: 3 × 4x and 3 × (2).
    2. Simplify to 12x + 6.

  7. H075(x − 3)

    M-ALG-007-WS01-H07

    Answer
    5x − 15
    Worked steps
    1. Multiply both terms by 5: 5 × 1x and 5 × (-3).
    2. Simplify to 5x − 15.

  8. H082(3x − 4)

    M-ALG-007-WS01-H08

    Answer
    6x − 8
    Worked steps
    1. Multiply both terms by 2: 2 × 3x and 2 × (-4).
    2. Simplify to 6x − 8.

  9. H09-2(x + 6)

    M-ALG-007-WS01-H09

    Answer
    -2x − 12
    Worked steps
    1. Multiply both terms by -2: -2 × 1x and -2 × (6).
    2. Simplify to -2x − 12.

  10. H10-3(2x − 5)

    M-ALG-007-WS01-H10

    Answer
    -6x + 15
    Worked steps
    1. Multiply both terms by -3: -3 × 2x and -3 × (-5).
    2. Simplify to -6x + 15.

Applied practice

  1. H11A rectangular floor is 3 m wide and (2x + 5) m long. Write an expanded expression for its area.

    M-ALG-007-WS01-H11

    Answer
    (6x + 15) m²
    Worked steps
    1. Area = 3(2x + 5).
    2. Multiply both terms by 3: area = (6x + 15) m².

  2. H12Six packs each contain (2x + 5) pencils. Eight pencils are removed from the total. Write a simplified expression for the number left.

    M-ALG-007-WS01-H12

    Answer
    12x + 22
    Worked steps
    1. Total before removing pencils = 6(2x + 5) = 12x + 30.
    2. Subtract 8: 12x + 30 − 8 = 12x + 22.